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Lee, Sungjay

/ School of Physics

High Energy Physics

Sungjay Lee is a theoretical physicist working mostly on Quantum Field Theory (QFT). This is a natural framework describing many different parts of physics, from particle physics, to condensed matter physics, and to statistical physics. To make fundamental theoretical advances in some of the most interesting problems in modern physics such as the strong nuclear force, strongly coupled systems of electrons, and quantum gravity, it is essential to understand QFT in the strongly coupled regime. Over the years, he has investigated new theoretical tools to understand the strong dynamics of supersymmetric field theory, conformal field theory, and string/M-theory.

We discuss the local (gauged) Weyl symmetry and its spontaneous breaking and apply it to model building beyond the standard model (SM) and inflation. In models with nonminimal couplings of the scalar fields to the Ricci scalar that are conformal invariant, the spontaneous generation by a scalar field(s) vacuum expectation value of a positive Newton constant demands a negative kinetic term for the scalar field or vice versa. This is naturally avoided in models with additional Weyl gauge symmetry. The Weyl gauge field omega(mu) couples to the scalar sector but not to the fermionic sector of a SM-like Lagrangian. The field omega(mu) undergoes a Stueckelberg mechanism and becomes massive after eating the (radial mode) would-be Goldstone field (dilaton rho) in the scalar sector. Before the decoupling of omega(mu), the dilaton can act as an UV regulator and maintain the Weyl symmetry at the quantum level, with relevance for solving the hierarchy problem. After the decoupling of omega(mu), the scalar potential depends only on the remaining (angular variables) scalar fields, which can be the Higgs field, inflaton, etc. We show that a successful inflation is then possible with one of these scalar fields identified as the inflaton. While our approach is derived in the Riemannian geometry with omega(mu) introduced to avoid ghosts, the natural framework is that of Weyl geometry, which for the same matter spectrum is shown to generate the same Lagrangian, up to a total derivative.

We constrain the spectrum of N = (1, 1) and N = (2, 2) superconformal field theories in two-dimensions by requiring the NS-NS sector partition function to be invariant under the congruence subgroup of the full modular group SL(2, Z). We employ semi-definite programming to find constraints on the allowed spectrum of operators with or without U(1) charges. Especially, the upper bounds on the twist gap for the noncurrent primaries exhibit interesting peaks, kinks, and plateau. We identify a number of candidate rational (S)CFTs realized at the numerical boundaries and find that they are realized as the solutions to modular differential equations associated to . Some of the candidate theories have been discussed by Hohn in the context of self-dual extremal vertex operator (super)algebra. We also obtain bounds for the charged operators and study their implications to the weak gravity conjecture in AdS(3).

We give a short review over recent works on modular constraints on the two-dimensional (supersymmetric) CFTs and their implications to the three-dimensional quantum gravity in anti de Sitter space via the holographic principle.

In gauge theories on a spacetime equipped with a circle, the holonomy variables, living in the Cartan torus, play special roles. With their periodic nature properly taken into account, we find that a supersymmetric gauge theory in d dimensions tends to reduce in the small radius limit to a disjoint sum of multiple (d -1) dimensional theories at distinct holonomies, called H-saddles. The phenomenon occurs regardless of the spacetime dimensions, and here we explore such H-saddles for d = 4 N = 1 theories on T-2 fibered over Sigma(g), in the limits of elongated T-2. This naturally generates novel relationships between 4d and 3d partition functions, including ones between 4d and 3d Witten indices, and also leads us to reexamine recent studies of the Cardy exponents and the Casimir energies and of their purported connections to the 4d anomalies.

We study codimension-two BPS defects in 2d N = (2, 2) supersymmetric gauge theories, focusing especially on those characterized by vortex-like singularities in the dynamical or non-dynamical gauge field. We classify possible SUSY-preserving boundary conditions on charged matter fields around the vortex defects, and derive a formula for defect correlators on the squashed sphere. We also prove an equivalence relation between vortex defects and 0d-2d coupled systems. Our defect correlators are shown to be consistent with the mirror symmetry duality between Abelian gauged linear sigma models and Landau-Ginzburg models, as well as that between the minimal model and its orbifold. We also study the vortex defects inserted at conical singularities.

We study constraints coming from the modular invariance of the partition function of two-dimensional conformal field theories. We constrain the spectrum of CFTs in the presence of holomorphic and anti-holomorphic currents using the semi-definite programming. In particular, we find the bounds on the twist gap for the non-current primaries depend dramatically on the presence of holomorphic currents, showing numerous kinks and peaks. Various rational CFTs are realized at the numerical boundary of the twist gap, saturating the upper limits on the degeneracies. Such theories include Wess-Zumino-Witten models for the Delignes exceptional series, the Monster CFT and the Baby Monster CFT. We also study modular constraints imposed by W-algebras of various type and observe that the bounds on the gap depend on the choice of W-algebra in the small central charge region.

Three-dimensional gauge theory T[G] arises on a domain wall between four-dimensional N = 4 SYM theories with the gauge groups G and its S-dual G(L). We argue that the N = 2* mass deformation of the bulk theory induces a mass-deformation of the theory T[G] on the wall. The partition functions of the theory T[SU(2)] and its mass-deformation on the three-sphere are shown to coincide with the transformation coefficient of Liouville one-point conformal block on torus under the S-duality.

We explore the low-energy dynamics of 1/2-BPS heavy particles coupled to the ABJM model via the Higgsing of M2-branes, with focus on physical understanding of the recently discovered 1/2-BPS Wilson loop operators. The low-energy theory of 1/2-BPS heavy particles turns out to have the U(N vertical bar N) supergauge symmetry, which explains the novel structure of the 1/2-BPS Wilson loop operator as a holonomy of a U(N vertical bar N) superconnection. We show that the supersymmetric transformation of the Wilson loop operator can be identified as a fermionic supergauge transformation, which leads to their invariance under half of the supersymmetry. We also argue that 1/2-BPS Wilson loop operators appear as 1/2-BPS vortices with vorticity 1/k. Such a vortex can be naturally interpreted as a membrane wrapping the Z(k) cycle once, or type IIA fundamental string.

We study spectrum of D = 2 N = (2, 2) QED with N + 1 massive charged chiral multiplets, with care given to precise supermultiplet countings. In the infrared the theory flows to CPN model with twisted masses, where we construct generic flavored kink solitons for the large mass regime, and study their quantum degeneracies. These kinks are qualitatively different and far more numerous than those of small mass regime, with features reminiscent of multi-pronged (p, q) string web, complete with the wall-crossing behavior. It has been also conjectured that spectrum of this theory is equivalent to the hypermultiplet spectrum of a certain D = 4 Seiberg-Witten theory. We find that the correspondence actually extends beyond hypermultiplets in D = 4, and that many of the relevant indices match. However, a D = 2 BPS state is typically mapped to several different kind of dyons whose individual supermultiplets are rather complicated; the match of index comes about only after summing over indices of these different dyons. We note general wall-crossing behavior of flavored BPS kink states, and compare it to those of D = 4 dyons.

We consider topological twisting of recently constructed Chern-Simons-matter theories in three dimensions with N = 4 or higher supersymmetry. We enumerate physically inequivalent twistings for each N, and find two different twistings for N = 4, one for N = 5, 6, and four for N = 8. We construct the two types of N = 4 topological theories, which we call A/B-models, in full detail. The A-model has been recently studied by Kapustin and Saulina. The B-model is new and it consists solely of a Chern-Simons term of a complex gauge field up to BRST-exact terms. We also compare the new theories with topological Yang-Mills theories and find some interesting connections. In particular, the A-model seems to off er a new perspective on Casson invariant and its relation to Rozansky-Witten theory.

We investigate the low energy physics of particles in the symmetric phase of the N = 6 mass-deformed ABJM theory in terms of the superconformal nonrelativistic field theory with 14 supercharges. They describe a certain kind of excitations on M2 branes in the background of external four-form flux. We study the nonrelativistic superconformal algebra and their representations by using the operator-state correspondence with the related harmonic oscillator Hamiltonian. We find the unitarity bounds on the scaling dimension and particle number of any local operator, and comment on subtleties in computing the superconformal Witten index that counts the chiral operators.

We discuss non-perturbative effects in the ABJM model due to monopole instantons. We begin by constructing the instanton solutions in the U(2) x U(2) model, explicitly, and computing the Euclidean action. The Wick-rotated Lagrangian is complex and its BPS monopole instantons are found to be a delicate version of the usual t Hooft-Polyakov monopole solutions. They are generically 1/3 BPS but become 1/2 BPS at special locus in the moduli space of two M2-branes, yet each instanton carries eight fermionic zero modes, regardless of the vacuum choice. The low energy effective action induced by monopole instantons are quartic order in derivatives. The resulting vertices are nonperturbative in 1/k, as expected, but are rational functions of the vacuum moduli. We also analyze the system of two M2-branes in the supergravity framework and compute the higher order interactions via 11-dimensional supergraviton exchange. The comparison of the two shows that the instanton vertices are precisely reproduced by this M2-brane picture, supporting the proposal that the ABJM model describes multiple M2-branes.

We find a 16-supersymmetric mass-deformed Bagger-Lambert theory with SO(4) x SO(4) global R symmetry. The R charge plays the role of the noncentral term in the superalgebra. This theory has one symmetric vacuum and two inequivalent broken sectors of vacua. Each sector of the broken symmetry has SO(4) geometry. We find the 1/2 BPS domain walls connecting the symmetric phase and any broken phase, and 1/4 BPS supertubelike objects, which may appear as anyonic q-balls in the symmetric phase or vortices in the broken phase. We also discuss mass deformations, which reduce the number of supersymmetries.

We consider the BPS dyonic instantons in the 5-dim supersymmetric Yang-Mills Chern-Simons theories. Its field theoretic structures and the moduli space dynamics in term of the ADHM data have been explored in detail. We find that the field theoretic Chern-Simons term leads to an effective magnetic field on instanton moduli space.

We extend the N = 4 superconformal Chern-Simons theories of Gaiotto and Witten to those with additional twisted hyper-multiplets. The new theories are generically linear quiver gauge theories with the two types of hyper-multiplets alternating between gauge groups. Our construction includes the Bagger-Lambert model of SO(4) gauge group. A family of abelian theories are identified with those proposed earlier in the context of the M-crystal model for M2-branes probing (C-2/Z(n))(2) orbifolds. Possible extension with non-abelian BF couplings and string/M-theory realization are briefly discussed.